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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Self similar flows in finite or infinite two dimensional geometries
Author: Espin Estevez, Leonardo Xavier
View Online: njit-etd2009-047
(xii, 92 pages ~ 5.4 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Papageorgiou, Demetrius T. (Committee chair)
Cummings, Linda Jane (Committee member)
Petropoulos, Peter G. (Committee member)
Rumschitzki, David Sheldon (Committee member)
Siegel, Michael (Committee member)
Date: 2009-05
Keywords: Applied math
Exact solutions
Fluid dynamics
Self-similar solutions
Numerical simulations
Stability analysis
Availability: Unrestricted

This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains.

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